Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, by adapting the work of Colding–Minicozzi^[11], we prove codimension bounds for ancient mean curvature flows by their tangent flow at −∞. In the case of the m-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at −∞.

中文翻译：

---

古代平均曲率流的余量界和刚度由-∞处的切线流动

受显式紧凑古代曲线缩短流的限制行为的启发，通过调整 Colding-Minicozzi ^[11]的工作，我们通过其切线流证明古代平均曲率流的余维界 -∞. 在这种情况下米-覆盖圆，我们应用这个界来证明一个强刚性定理。此外，我们通过表明在足够快速收敛的假设下扩展了这一范式，紧凑的古代平均曲率流与其在 -∞.